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AbstractFor building a real time marine power system

simulator, models of fast calculation and high precision of

marine power system are needed. Because there are abilities

of learning and batch operation with artificial neural

networks (ANN), it is fit for using ANN to build a real time

marine diesel generator model for marine power system

simulator. In this paper, radial basis function neural networks

(RBF NN) was used for building model of marine diesel engine

generator. RBF NN is universal approximation neural

network. There is ability to approximate a nonlinear function

with RBF NN. According to working principles of diesel

generator, parameters of excitation current/voltage and diesel

engine mechanical torque are as inputs of RBF NN,

parameters of terminal voltage current and frequency of

generator are as outputs for RBF NN training. The type of

supervised learning of center selection strategy was used for

the RBF NN learning method. An approximated model of

marine diesel generator is built in high precision result with

99 hidden neurons of RBF NN.

I. INTRODUCTION

CCORDING to STCW78/95 international convention,

established by the International Maritime

Organization (IMO), marine engineers on automatic

ocean-ships must be advance through marine power system

simulator training. Marine power system is different with

shore power system because the generator is drove by large

capacity diesel engine. For building a real time marine

power system simulator, mathematical model of marine

diesel generator is needed. Two factors about the real time

model are considered. One factor is calculation speed of

model. Another factor is precision of model. The factors are

important to response characteristics of real time marine

power system simulator. Because theory model of electrical

generator is so complex, it is not fit for simulator

Weifeng Shi, Associate Prof., Dept. of Electric Automation. SMU.

Pudong Dadao 1550 hao, 1064#. 200135, Shanghai, China.

Tel: 0086-21-58850762, Fax: 0086-21-58853909,

e-mail: wfshi@shmtu.edu.cn,

Jianmin Yang, Dept. of Electric Automation. SMU. Shanghai PuDongDaDao 1550 Hao, 200135, Shanghai, China.

Tel: 0086-21-58855200-2211,

e-mail: yang.jian.min@163.com,

Tianhao Tang, Prof. Dept. of Electric Automation. SMU.

Member of IEEE. Pudong Dadao 1550 hao. 200135, Shanghai, China.

Tel: 0086-21-58855200-4228, Fax: 0086-21-58853909,

e-mail: thtang@ieee.org,

calculating by DSP. ANN provides opportunity for

improving the precision and fast calculation speed to real

time marine diesel generator model. Radial basis function

neural network (RBF NN) is broad to uniformly

approximate any continuous function [4]. There is ability to

approximate nonlinear model with RBF NN. In the paper,

RBF NN was used for marine diesel generator modeling of

real time power system simulator.

II. NEURON MODEL ANDNETWORK

ARCHITECTURE OF RBF NN

Neuron model of RBF NN is showed in Fig.1 with p

inputs. HereR is number of elements in input vector. The

dist box in this figure accepts the input vectorp andthe single row input weight matrix, and produces the dot

product of the two [1]. The net input to the transfer function

is the vector distance between its weight vectorw and the

input vector p, multiplied by bias b. The relationship

between input and output is:

p = [p1 p2 p3 pR ]

w = [w1,1 w1,2 w1,3 w1,R]

)][(1 bfa = pw

Select Gaussian function as transfer function. The functionfor a radial basis neuron is:

2

)(1nenf = (1)

The output ofa is:

])([ 2bexpa = pw

2

1

maxd

mb =

Here, m1 is the number of centers and dmax is the maximum

distance between the chosen centers.

RBF NN Based Marine Diesel Engine

Generator Modeling

Weifeng Shi, Jianmin Yang, Tianhao Tang,Member, IEEE

A

Input layer Radial Basis Neuron

Fig. 1. Neuron model of RBF NN

2005 American Control ConferenceJune 8-10, 2005. Portland, OR, USA

0-7803-9098-9/05/$25.00 2005 AACC

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RBF NN consists of three layers include input layer withnetworks. Fig.2 shows network architecture of radial basis

networks. The input layer is made up of source nodes that

connect the network to its environment. The second layer,

the only hidden layer, it is radial basis layer ofS1

neurons.Here S1 is number of neurons in hidden layer. It applies a

nonlinear transformation from the input space to the hidden

space, in most applications the hidden space is of high

dimensionality. The dist box in this figure accepts theinput vector p and the input weight matrix IW1,1 and

produces a vector having S1

elements. The elements are thedistances between the input vector and vectorIW1,1 formed

from the rows of the input weight matrix [1]. And another is

output linear layer ofS2

neurons. The output layer is linearlayer.

According to network architecture of RBF NN in Fig.2,

the output of radial basis layer and linear layer can becalculate as:

])p([ IW 211,1

1exp ii bia =

)(21

1,222

baa LWy +== f

In Fig.2, R is number of elements in input vector, S1 isnumber of neurons in radial basis layer, S2 is number of

neurons in linear layer. ai1

is the ith element ofa1. iIW1,1 is a

vector made of the ith row ofIW1,1.f2 is a linear function.

An important point is the fact that the dimension of the

hidden space is directly related to the capacity of thenetwork to approximate a smooth input-output mapping;

the higher the dimension of the hidden space, the more

accurate the approximation will be [3].

III. MARINE ELECTRIC POWERSYSTEM INTRODUCE

The power supply and control system are becoming more

complex now the electrical capacity of automatedocean-going ships is growing larger. Fig. 3 shows the

configuration of electric power system of a large marine

container ship. This is an AC440V (3-60Hz) powernetwork system. The capacity of each diesel generator is

2850kVA, 3657A. There is an emergency diesel generator

(325kVA, 417A) with the system. About electric loads,there are side-thruster (2200kW, 465A), steering gear,

refrigerated container and so on. The dynamic

characteristic of marine power system depends on the diesel

engine generator. For power system simulator, model of the

diesel engine generator is the most important section.

IV. MARINE DIESEL ENGINE GENERATOR

MODELING BASED ON RBF NN

A. Diesel Generator Modeling Method

Three layers networks were formed with one input layer

one hidden layer and one output layer as Fig. 2. The neural

networks based model of generator depends on the weights

between neural elements. Supervised learning is used in the

system training. We can train a neural network by adjusting

the values of the weights according to error. After that an

input tend to a specific target output.

A supervised neural network was pursued in a variety of

weights. The supervised training of the neural networks can

be viewed as a curve-fitting process. For approach to themarine diesel generator model, a configuration diagram of

RBF NN of diesel generator modeling and training is shown

in Fig. 4. First step is to select input and output parameters

of generator. We selected that the input parameters are

excitation current/voltage (vt) and diesel engine mechanical

torque (Pm). The output parameters are terminal voltage (v),

current (i) and frequency ( f ) of generator. Through

measuring and recording, a set of data will be obtained as

sampling data for training. The measured data vector is x.

Fig. 2. Network architecture of RBF NN

Input layer Radial Basis layer Linear layer

Fig. 3 Configuration of the electric power system

SIDE THRUSTER2200kW 465A

(L)220V F P

(A)220VF P

REF.

Container

General

Feed

No.1Steergear

No.2Steergear

GSP

1~3

AC450V 360Hz2500kW

AC450V 360Hz260kW

3VA440/3300V

1VA440/220V

1VA440/220V

ST

AH-40C AH-40C AH-40CAME-6AH-40C

MSB ESB

D/G1 D/G2 D/G3 D/G4 EG

M

Fig. 4. Configuration diagram of RBF NN training

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The input p connected to RBF NN through a tapped delay

line. The input vectorp of RBF NN is:

p = [vt Pm v' i' f ']

The output vectory of RBF NN is:

y = [v1 i1 f1 ]

Such input value and desire value pair vectors were used for

training a network in supervised learning. The network isadjusted, based on error of output vectory = [v1 i1 f1 ] and

desired response vectord = [v i f], until the network output

matches the desired response. So the number of elements in

input vector (R) is five. The number of neurons in linear

layer (S2) is three.

B. Learning Strategies of RBF NN

There are different learning strategies that we can follow

in training of a RBF NN, depending on how the centers of

the radial-basis functions of the network are specified. Here

supervised selection of centers learning strategies was used.

The centers of the radial basis functions and other

parameters of the network in supervised learning process.We define the value of cost function as:

=

=

N

jje

1

2

2

1 (2)

Here N is the size of the training sample used to do the

learning, and ej is the error defined by:

=

==

2

1

* )(S

i Cijijjjjjj

i

GwdFdyde tpp (3)

The requirement is to find the parameters wi, ti, and i-1 (the

latter being related to the norm-weighting matrix Ci) so as

to minimize . Here, wi is linear weights, ti is positions of

centers of a radial-basis function, i-1 is spread of centers.

The results of this minimization are summarized as follow:(1) Linear weights (output layer)

=

=

N

jCijj

ii

nnenw

n

1

))(()()(

)(tp

(4)

1

1,,2,1,

)(

)()()1( Si

nw

nnwnw

i

ii =

=+

(5)

(2) Positions of centers (hidden layer)

[ ])()())((')()(2)(

)(

1

1nnnnenw

n

nii

N

jiCijji

ii

tptpt

=

=

(6)

1

2,,2,1,

)(

)()()1( Si

n

nntnt

i

ii =

=+

t

(7)

(3) Spreads of centers (hidden layer)

)())((')()()(

)(

11

nQnnenwn

njiCij

N

j

ji

i

i

tp =

=

(8)

T)]()][([)( nnnQijijji tptp = (9)

=+

1

13

1

)(

)()()1(

i

i

in

nnn

(10)

Here, n is steps number of iteration. ej(n) is the error

signal of output unitj at step n. The )(' is first derivative

of the Greens function )( with respect to its argument.

The 1, 2 and 3 are three coefficients of learning. Thelearning-rates were depended on the value of them

respectively.

The training process of RBF NN modeling as follow:

(1) Endow with initial values to all weights and bias.

(2) Present input and output sample data for RBF NNtraining.

(3) Calculate the outputs of RBF NN according to

inputs, weight and bias. When the value of cost

function between sample data to output of RBF

NN is little than permission value, the training

process finishes. Otherwise shift to step (4).

(4) According to difference between RBF NN output

value and expectation value, the weights and bias

will be adjusted.

(5) Go back to step (2).

C. Modeling Results of Marine Diesel Generator

The parameters of input and output were measured assampling data, and used for RBF NN offline training. We

selected some different running states of marine power

system, such as diesel engine generator starting, a general

pump (240kW, 440V) of power system running, a

side-thruster (2200kW, 3300V) starting and three-phases

short circuit ground fault.

After training, the diesel engine generator model of RBF

NN was built in network weights function. There are 99 (S1)

hidden neurons with one RBF NN model for normal

operating model. As example, terminal voltage parameter

of generator is selected to demonstrate the precision of

model in normal operating. The parameter of terminal

voltage is per unit value in diagram. The error is desired

value minus output value of RBF NN model. The axis of

horizontal is time (t). It is a relationship between period

time (T) of sampling and size (N) of the training samples.

There is t = T N. Some approximated results were

obtained. The first approximated result is diesel engine

starting. Fig. 5 shows voltage of generator and its error

between desired value and output value of RBF NN model

when diesel engine generator starting. Fig. 6 shows

terminal voltage of generator and error when lubrication

pump is starting. Fig. 7 shows terminal voltage of generator

and error when side-thruster motor is starting. For power

system three-phases short circuit ground fault, the faultprocess likes this. A ground fault occurs from a general

pump. A large overload current was produced, and terminal

voltage of generator was full down. After that the

protection unit cut off this general pump because of

overload current. In the end, the terminal voltage of

generator was recovered. Fig. 8 shows terminal voltage of

generator and error with RBF NN model when three-phase

grounded fault happened. From the recorded data and error

curve all above, the error value is limited in 5104. So the

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diesel engine generator model approximated by RBF NN

with high precision results.

V. APPLICATION OF MARINE DIESEL ENGINE

GENERATORMODEL TO A REAL TIME SIMULATOR

For building a real time marine power system simulator,

ANN model of synchronous generator has been obtained.

Fig. 5. Voltage and its error with RBF NN modelwhen diesel engine generator is starting

Error(pu)

Time(s)

Voltage(pu)

Time(s)

* output of NN

real data

Fig. 7. Voltage and its error with RBF NN modelwhen side-thruster motor is starting

Error(pu)

Time(s)

Voltage(pu)

Time(s)

* output of NN real data

Fig. 6. Voltage and its error with RBF NN modelwhen lubrication pump is starting

E

rror(pu)

Time(s)

Voltage(pu)

Time(s)

* output of NN real data

Fig. 8. Voltage and its error with RBF NN modelwhen three-phase grounded fault happened

Error(pu)

Time(s)

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After that the model operation program is downloaded to a

digital signal processor (DSP). Fig. 9 shows a part of

configuration between controller and models for real time

marine power system simulator. Logical controller is used

for diesel engine starting and stopping. Speed controller is

used for constant value control of diesel engine rotational

speed. Voltage regulator is used for terminal voltage

control of generator. Generally the rule of regulators are

PID controllers. Through testing by TMS320LF2407 DSP

(30MIPS), the operating period time of model is little than

158 microseconds with 99 hidden neural nodes of RBF

NN.

In the real time marine power system simulator system,

the control computer was an industrial microcomputer. Adata acquisition and control system is used for signals

input and output. Generally the input signals are rotational

speed (rpm) of diesel engine, voltage (V) and current (A)

of generator. The output signals are oil supply, excitation

voltage or current. The RBF NN generator model produces

voltage signal and current signal to voltage regulator. All

parameters were display through control computer.

VI. CONCLUSION

Because generator system is a nonlinear system, the RBFNN was used for marine diesel engine generator modeling,

the model approximated with good precision. The

calculation speed is satisfactory using RBF NN generatormodel. The advantage of using RBF NN to build a marine

generator model is that the algorithm is simple and fast. It isfit for DSP calculating. The disadvantage of the method isthat the generalization of system is not so satisfactory. The

ability of RBF NN generalization is not enough for all

status of generator in one model especially for failurerunning state of generator. In normal operating mode and

fault operating mode of real time power system simulator,

we had to use two different models. One model is used fornormal operating. Other model is used for fault operating.

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Fig. 9. Part structure of real time simulator

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